Published October 21, 2025 | Version Published
Journal Article Open

Late-Time Tails in Nonlinear Evolutions of Merging Black Holes

  • 1. ROR icon University of Copenhagen
  • 2. ROR icon University of Lisbon
  • 3. ROR icon University of Birmingham
  • 4. ROR icon Friedrich Schiller University Jena
  • 5. ROR icon INFN Sezione di Torino
  • 6. ROR icon King's College London
  • 7. ROR icon Cornell University
  • 8. ROR icon University of Mississippi
  • 9. ROR icon California Institute of Technology
  • 10. ROR icon Institut des Hautes Études Scientifiques
  • 11. ROR icon Max Planck Institute for Gravitational Physics
  • 12. ROR icon University of Maryland, College Park

Abstract

We uncover late-time gravitational-wave tails in fully nonlinear 3+1 dimensional numerical relativity simulations of merging black holes, using the highly accurate p code. We achieve this result by exploiting the strong magnification of late-time tails due to binary eccentricity, recently observed in perturbative evolutions, and showcase here the tail presence in head-on configurations for several mass ratios close to unity. We validate the result through a large battery of numerical tests and detailed comparison with a perturbative evolution, which display striking agreement with full nonlinear ones in the ringdown regime, and very similar tail morphologies. Our results offer yet another confirmation of the highly predictive power of black hole perturbation theory in the presence of a source, even when applied to nonlinear solutions. The late-time tail signal is much more prominent than anticipated until recently, and possibly within reach of gravitational-wave detector measurements, unlocking observational investigations of an additional set of general relativistic predictions on the long-range gravitational dynamics.

Copyright and License

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Acknowledgement

M. D. A. expresses her gratitude to Perimeter Institute for its kind hospitality during the final stages of the manuscript preparation. M. D. A. also thanks Sizheng Ma and Luis Lehner for stimulating discussions on the topic during the visit. S. A. gratefully acknowledges the warm hospitality of the Niels Bohr Institute, where this work was initiated. G. C. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 847523 “INTERACTIONS.” The Center of Gravity is a Center of Excellence funded by the Danish National Research Foundation under Grant No. 184. We acknowledge support from the Villum Investigator program by the VILLUM Foundation (Grant No. VIL37766) and the DNRF Chair program (Grant No. DNRF162) by the Danish National Research Foundation. H. R. R. and V. C. acknowledge financial support provided under the European Union’s H2020 ERC Advanced Grant “Black holes: gravitational engines of discovery” Grant Agreement No. Gravitas-101052587. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreements No. 101007855 and No. 101131233. K. M. is supported by NASA through the NASA Hubble Fellowship Grant No. HST-HF2-51562.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA Contract No. NAS5-26555. S. A. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG) project “GROOVHY” (BE 6301/5-1 Projektnummer: 523180871). L. C. S. acknowledges support from NSF CAREER Award No. PHY–2047382 and a Sloan Foundation Research Fellowship. S. B. acknowledges support by the EU Horizon under ERC Consolidator Grant No. InspiReM-101043372 and from the Deutsche Forschungsgemeinschaft (DFG) project “GROOHVY” (BE 6301/5-1 Projektnummer: 523180871). A. Z. is supported by the National Science Foundation under Grant No. 2309084. This material is based upon work supported by the National Science Foundation under Grants No. PHY-2407742, No. PHY-2207342, and No. OAC-2209655 at Cornell. This work was supported by the Sherman Fairchild Foundation at Cornell. This work was supported in part by the Sherman Fairchild Foundation and by NSF Grants No. PHY-2309211, No. PHY-2309231, and No. OAC-2209656 at Caltech. Simulations have been carried out on the Frontera computing system within the Texas Advanced Computing Center (TACC) Grant No. PHY20018, “Gravitational Waves from Compact Binaries: Computational Contributions to LIGO.”

Data Availability

spec simulation data are available from Caltech Data [90–95,133–140] and can also be accessed through the sxs python package [89,131].

Supplemental Material

Supplemental material present a series of tests to confirm the robustness of the numerical results shown in the paper.

Additional Information

The views and opinions expressed are those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Additional details

Related works

Is new version of
Discussion Paper: arXiv:2412.06887 (arXiv)
Is supplemented by
Supplemental Material: https://journals.aps.org/prl/supplemental/10.1103/2brx-xnyr/supplemental_material.pdf (URL)

Funding

European Commission
847523
Danish National Research Foundation
184
Villum Fonden
VIL37766
Danish National Research Foundation
DNRF162
European Research Council
Gravitas-101052587
European Commission
101007855
European Commission
101131233
National Aeronautics and Space Administration
HST-HF2-51562.001-A
National Aeronautics and Space Administration
NAS5-26555
Space Telescope Science Institute
Deutsche Forschungsgemeinschaft
523180871
National Science Foundation
PHY–2047382
Alfred P. Sloan Foundation
European Research Council
InspiReM-101043372
National Science Foundation
2309084
National Science Foundation
PHY-2407742
National Science Foundation
PHY-2207342
National Science Foundation
OAC-2209655
Cornell University
Sherman Fairchild Foundation
National Science Foundation
PHY-2309231
National Science Foundation
PHY-2309211
National Science Foundation
OAC-2209656
California Institute of Technology
Texas Advanced Computing Center
PHY20018

Dates

Accepted
2025-09-04

Caltech Custom Metadata

Caltech groups
TAPIR, Walter Burke Institute for Theoretical Physics, Division of Physics, Mathematics and Astronomy (PMA)
Publication Status
Published